Os retornos aparentemente são estacionários. Iremos fazer o teste de ljung-box para confirmar o ruÃdo branco nos resÃduos e também realizar o teste de raÃz unitária.
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## Box-Ljung test
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## data: df
## X-squared = 26.875, df = 1, p-value = 2.171e-07
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## Augmented Dickey-Fuller Test
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## data: df_box$ret.closing.prices
## Dickey-Fuller = -13.704, Lag order = 14, p-value = 0.01
## alternative hypothesis: stationary
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## ARCH LM-test; Null hypothesis: no ARCH effects
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## data: df_box$ret.closing.prices
## Chi-squared = 101.06, df = 12, p-value = 3.454e-16
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## Box-Ljung test
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## data: df
## X-squared = 68.531, df = 1, p-value < 2.2e-16
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##
## Augmented Dickey-Fuller Test
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## data: df_box$ret.closing.prices
## Dickey-Fuller = -15, Lag order = 14, p-value = 0.01
## alternative hypothesis: stationary
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##
## ARCH LM-test; Null hypothesis: no ARCH effects
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## data: df_box$ret.closing.prices
## Chi-squared = 462.56, df = 12, p-value < 2.2e-16
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## Box-Ljung test
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## data: df
## X-squared = 0.17805, df = 1, p-value = 0.6731
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##
## Augmented Dickey-Fuller Test
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## data: df_box$ret.closing.prices
## Dickey-Fuller = -13.735, Lag order = 14, p-value = 0.01
## alternative hypothesis: stationary
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##
## ARCH LM-test; Null hypothesis: no ARCH effects
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## data: df_box$ret.closing.prices
## Chi-squared = 101.18, df = 12, p-value = 3.263e-16
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## Box-Ljung test
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## data: df
## X-squared = 0.020172, df = 1, p-value = 0.8871
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##
## Augmented Dickey-Fuller Test
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## data: df_box$ret.closing.prices
## Dickey-Fuller = -13.687, Lag order = 14, p-value = 0.01
## alternative hypothesis: stationary
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##
## ARCH LM-test; Null hypothesis: no ARCH effects
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## data: df_box$ret.closing.prices
## Chi-squared = 449.86, df = 12, p-value < 2.2e-16
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## Box-Ljung test
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## data: df
## X-squared = 9.0881, df = 1, p-value = 0.002573
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##
## Augmented Dickey-Fuller Test
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## data: df_box$ret.closing.prices
## Dickey-Fuller = -13.57, Lag order = 14, p-value = 0.01
## alternative hypothesis: stationary
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##
## ARCH LM-test; Null hypothesis: no ARCH effects
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## data: df_box$ret.closing.prices
## Chi-squared = 620.61, df = 12, p-value < 2.2e-16
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## Box-Ljung test
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## data: df
## X-squared = 46.137, df = 1, p-value = 1.103e-11
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##
## Augmented Dickey-Fuller Test
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## data: df_box$ret.closing.prices
## Dickey-Fuller = -15.484, Lag order = 14, p-value = 0.01
## alternative hypothesis: stationary
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##
## ARCH LM-test; Null hypothesis: no ARCH effects
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## data: df_box$ret.closing.prices
## Chi-squared = 463.78, df = 12, p-value < 2.2e-16